(Each question 1 marks)

Question 11 Mark

Find the degree measure corresponding to the following radian measures: $(\text{Use}\ \pi=\frac{22}{7})$ $\frac{-5\pi}{6}$

Answer

We have, $\pi$ reduans = 180º $1^{\text{c}}=\big(\frac{180}{\pi}\big)^{\circ}$ Now, $\Big(\frac{-5\pi}{6}\Big)^{\text{c}}=\Big(\frac{-5\pi}{6}\times\frac{180}{\pi}\Big)^{\circ}$ $=-150^{\circ}$

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Question 21 Mark

Find the radian measure corresponding to the following degree measures: 7°30'

Answer

We have, $180^{\circ}=\pi^{\text{c}}$ $\therefore 1^{\circ}=\Big(\frac{\pi}{180}\Big)^{\text{c}}$ Now, $7^{\circ}30^{'}=\Big(7\times\frac{\pi}{180}\Big)^{\text{c}}\times\Big(\frac{30}{60}\Big)^{\circ}$ $=\Big(7\frac{1}{2}\Big)^{\circ}\times\Big(\frac{\pi}{180}\Big)^{\text{c}}$ $=\Big(\frac{15}{2}\times\frac{\pi}{180}\Big)^{\text{c}}$ $=\frac{\pi}{24}$

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Question 31 Mark

Find the radian measure corresponding to the following degree measures: 300°

Answer

We have, $180^{\circ}=\pi^{\circ}$ $\therefore 1^{\circ}=\Big(\frac{\pi}{180}\Big)^{\text{c}}$ Now, $300^{\circ}=300\times\frac{\pi}{180}$ $=\frac{5\pi}{3}$

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Question 41 Mark

Find the radian measure corresponding to the following degree measures: 125°30'

Answer

We have, $180^{\circ}=\pi^{\text{c}}$ $\therefore 1^{\circ}=\Big(\frac{\pi}{180}\Big)^{\text{c}}$ Now, $125^{\circ}30^{'}=125^{\circ}\Big(\frac{30}{60}\Big)^{\circ}$ $=\Big(125\frac{1}{2}\Big)^{\circ}$ $=\Big(\frac{251}{2}\times\frac{\pi}{180}\Big)^{\text{c}}$ $=\frac{251\pi}{360}$

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Question 51 Mark

Find the degree measure corresponding to the following radian measures: $(\text{Use}\ \pi=\frac{22}{7})$ $\big(\frac{18\pi}{5}\big)$

Answer

We have, $\pi$ reduans = 180º $1^{\text{c}}=\big(\frac{180}{\pi}\big)^{\circ}$ Now, $\Big(\frac{18\pi}{5}\Big)^{\text{c}}=\Big(\frac{18\pi}{5}\times\frac{180}{\pi}\Big)^{\circ}$ $=648^{\circ}$

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Question 61 Mark

Find the radian measure corresponding to the following degree measures: 35°

Answer

We have, $180^{\circ}=\pi^{\circ}$ $\therefore 1^{\circ}=\Big(\frac{\pi}{180}\Big)^{\text{c}}$ Now, $35^{\circ}=35\times\frac{\pi}{180}$ $=\frac{7\pi}{36}$

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Question 71 Mark

Find the radian measure corresponding to the following degree measures: -56°

Answer

We have, $180^{\circ}=\pi^{\text{c}}$ $\therefore 1^{\circ}=\Big(\frac{\pi}{180}\Big)^{\text{c}}$ Now, $-56^{\circ}=-56\times\frac{\pi}{180}$ $=\frac{-14\pi}{45}$

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Question 81 Mark

Find the degree measure corresponding to the following radian measures: $(\text{Use}\ \pi=\frac{22}{7}) (-3)^c$

Answer

We have, $\pi$ reduans = 180º $1^{\text{c}}=\big(\frac{180}{\pi}\big)^{\circ}$ Now, $(-3)^{\text{c}}=\Big(-3\times\frac{180}{\pi}\Big)^{\circ}$ $=\Big(\frac{180}{22}\times7\times-3\Big)^{\circ}$ $=\Big(-171\frac{9}{11}\Big)^{\circ}$ $=-171^{\circ}\Big(\frac{9}{11}\times60\Big)^{'}$ $=-171^{\circ}49^{'}5^{"}$

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Question 91 Mark

Find the degree measure corresponding to the following radian measures: $(\text{Use}\ \pi=\frac{22}{7})$ $\frac{9\pi}{5}$

Answer

We have, $\pi$ reduans = 180º $1^{\text{c}}=\big(\frac{180}{\pi}\big)^{\circ}$ Now, $\Big(\frac{9\pi}{5}\times\frac{180}{\pi}\Big)^{\circ}$ $=324^{\circ}$

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Question 101 Mark

Find the radian measure corresponding to the following degree measures: 135°

Answer

We have, $180^{\circ}=\pi^{\text{c}}$ $\therefore 1^{\circ}=\Big(\frac{\pi}{180}\Big)^{\text{c}}$ Now, $135^{\circ}=135\times\frac{\pi}{180}$ $=\frac{3\pi}{4}$

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Question 111 Mark

Find the degree measure corresponding to the following radian measures: $(\text{Use}\ \pi=\frac{22}{7})$ $1^\text{c}$

Answer

We have, $\pi$ reduans = 180º $1^{\text{c}}=\big(\frac{180}{\pi}\big)^{\circ}$ Now, $(1)^{\text{c}}=\Big(1\times\frac{180}{\pi}\Big)^{\circ}$ $=1\times\frac{180\times7}{22}$ $=57^{\circ}\Big(\frac{3}{11}\times60\Big)$ $=57^{\circ}16^{'}\Big(\frac{4}{11}\times60\Big)^{"}$ $=57^{\circ}16^{'}21^{"}$

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Question 121 Mark

Find the degree measure corresponding to the following radian measures: $(\text{Use}\ \pi=\frac{22}{7}) 11^c$

Answer

We have, $\pi$ reduans = 180º $1^{\text{c}}=\big(\frac{180}{\pi}\big)^{\circ}$ Now, $(11)^{\text{c}}=\Big(11\times\frac{180}{\pi}\Big)^{\circ}$ $=\Big(11\times180\times\frac{7}{22}\Big)^{\circ}$ $=630^{\circ}$

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Question 131 Mark

Find the radian measure corresponding to the following degree measures: -300°

Answer

We have, $180^{\circ}=\pi^{\text{c}}$ $\therefore 1^{\circ}=\Big(\frac{\pi}{180}\Big)^{\text{c}}$ Now, $-300^{\circ}=-300\times\frac{\pi}{180}$ $=\frac{-5\pi}{3}$

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